DERIVATIVES OF INVERSE FUNCTIONS GIFT 2004
1. Let g ( x )  x 5  3 x  2, and let g 1 denote the inverse of g . Then g 1   2  is equal to:
 
A)
1
83
2. Let f ( x ) 
A)
4
31
B)
1
8
C) 1
E ) 83
1 3
x  x  1, and let f 1 denote the inverse of f . Then f 1   3  is equal to:
4
 
1
6
B)
1
4
C)
3. Let f ( x )  x 5  x. Find the value of
A) 81
D) 8
B) 6
E)
35
4
d 1
f ( x ) at x = 2.
dx
1
81
C)
1
3
D)
D)
1
6
E) 
1
6
4. Let h( x )  x 3  2x  1, and let h 1 denote the inverse of h . Then h 1   2  is equal to:
 
A) 14
B) 5
5. If f (4)  5 and f '(4) 
A)
1
5
B)
1
4
6. If g (7)  3 and g (3) 
A)
3
4
B)
5
6
C)
1
5
2
, then calculate:
3
C)
2
3
D)
1
9
E)
f  (5).
1
D)
3
2
E) 4
5
3
and g (7)  , then g 1  (3)  ?
6
4
 
C)
6
5
C 2004 Reardon Inverse Gifts, Inc.
D)
4
3
E)
1
7
1
14
7. Let f ( x )  3 x 4  x and let g be the inverse function of f . What is the value of g (2)?
A)
1
2
B) 
1
11
C)
1
11
D)
1
13
E) 
1
13
8. Let f ( x )  x 5  1 and let g be the inverse function of f . What is the value of g (0)?
1
C) 1
D ) g (0) does not exist
5
E) g (0) cannot be determined from the given information
A)  1
B)
9. The following table shows the values of differentiable functions f and g.
g
g
x
f
f
1
2
5
3
1
2
2
3
1
0
4
3
4
2
2
3
4
6
4
3
1
2
If H ( x )  f 1( x ), then H (3) equals
A) 
1
16
B) 
1
8
C) 
1
2
D)
1
2
E) 1
10. The following table shows the values of differentiable functions f and g.
g
g
x
f
f
6
1
1
2
1
2
0
1
3
5
1
1
2
3
4
4
2
3
4
7
3
If H ( x )  f 1( x ), then H (1) equals
A) 1
B) 0
C ) undefined
C 2004 Reardon Inverse Gifts, Inc.
D)
1
2
E) 1
11. Let f ( x )  x 3 
A)
1
13
1
4
 
1
6
B)
12. Let h( x ) 
A)
4
and let f 1 denote the inverse of f . Then f 1   6  is equal to:
x
C)
1
12
D) 
1
12
E) 
1
6
x  4 and let h 1 denote the inverse of h . Then h 1   2  is equal to:
 
1
8
B)
C) 8
13. Let f ( x )  sin x, 

2
x

2
D) 4
1
2
E)
, and let g be the inverse function of f . What is the value
 1
of g    ?
2
A)
2
3
B)
3
2
C)
1
2
D) 2
14. Let g ( x )  2x 3  x 2  1. Find the value of
A)
1
20
B)
1
13
15. If h(2)   3, h(2) 
A)
1
4
B)
1
3
E)
6

d 1
g ( x ) at x = 13.
dx
C ) 13
D ) 20
E)
1
1
, h( 3)  . Compute h 1  ( 3)
4
3
 
C) 4
E) 
D) 3
1
3
Answers (most of them should be correct, I hope  )
1. B
2. C
3. D
4. C
5. D
6. D
7. B
8. B
9. E
10. E
11. A
12. D
13. A
14. A
15. C
C 2004 Reardon Inverse Gifts, Inc.
1
5